The present invention relates to electronics circuits, and more particularly to impedance matching networks that reduce intermodulation distortion of active circuits.
Active circuits, such as low noise amplifiers (LNAs) and power amplifiers (PAs), are commonly used in many electronics circuits, including receivers and transmitters of communications systems. The performance of an active circuit can be quantified by its linearity, noise figure, power consumption, and so on. Generally, these characteristics impose conflicting design considerations.
A memoryless active circuit can be approximated by the following transfer function: EQU y(x)=a.sub.1 .multidot.x+a.sub.2 .multidot.x.sup.2 +a.sub.3 .multidot.x.sup.3 +higher order terms, Eq (1)
where x is the input signal, y(x) is the output signal, and a.sub.1, a.sub.2, and a.sub.3 are coefficients that define the linearity of the active circuit. To simplify the analysis, the higher order terms (i.e., terms above third order) are typically ignored. For an ideal linear active circuit, coefficients a.sub.2 and a.sub.3 are 0.0 and the output signal is simply the input signal scaled by a.sub.1. However, all active circuits experience some amounts of nonlinearity, which is quantified by coefficients a.sub.2 and a.sub.3. Coefficient a.sub.2 defines the amount of second-order nonlinearity and coefficient a.sub.3 defines the amount of third-order nonlinearity.
Active circuits are used in narrow band communications systems that operate on an input RF signal having a predetermined bandwidth and center frequency. The input RF signal typically comprises the desired signal and other undesired signals located throughout the frequency spectrum. Nonlinearity within the active circuits causes intermodulation of the undesired signals, resulting in products that may fall into the desired signal band.
As an example, consider an input RF signal that includes a desired signal m(t) centered at f.sub.d and undesired (i.e., spurious) signals at f.sub.1 and f.sub.2. The input RF signal can be expressed as: EQU x(t)=m(t)+g.sub.1 .multidot.cos(.omega..sub.1 t)+g.sub.2 .multidot.cos(.omega..sub.2 t). Eq (2)
When the input RF signal x(t) is provided to an active circuit having the transfer function of equation (1), where a.sub.2 and a.sub.3 are non-zero values, intermodulation products are generated.
FIG. 1A is a diagram illustrating the input RF signal and the intermodulation products. Specifically, the second-order nonlinearity of the active circuit (i.e., caused by the x.sup.2 term in equation 1) creates second-order intermodulation (IM2) products at various frequencies. The IM2 products include those at the frequencies (f.sub.2 -f.sub.1), (2.multidot.f.sub.1), (2.multidot.f.sub.2), and (f.sub.1 +f.sub.2) due to the undesired signals. These IM2 products appear at the output of the active circuit and also appear at the input of the active circuit due to the non-linear input impedance of the active circuit and the coupling between the output and input. The same second-order nonlinearity of the active circuit then mixes these IM2 products with the original undesired signals to produce third-order intermodulation (IM3) products at many frequencies, including those that fall into the desired band. Additionally, the third-order nonlinearity of the active circuit (e.g., caused by the x.sup.3 term in equation 1) creates IM3 products at the same frequencies as the IM3 products from the second order nonlinearity. The IM3 products that may fall into the desired band are those at the frequencies (2.multidot.f.sub.2 -f.sub.1) and (2.multidot.f.sub.1 -f.sub.2).
As a specific example, assume f.sub.1 =880 MHz, f.sub.2 =881 MHz, and f.sub.d =882 MHz. The second-order nonlinearity of the active circuit generates IM2 products appearing at (f.sub.2 -f.sub.1)=1 MHz, (2.multidot.f.sub.1)=1760 MHz, (2.multidot.f.sub.2)=1762 MHz, and (f.sub.2 +f.sub.1)=1761 MHz. Some of these IM2 products mix with the original undesired signals to produce IM3 products at the desired signal frequency f.sub.d. Specifically, the IM2 product at (f.sub.2 -f.sub.1) mixes with the undesired signal at f.sub.2 to generate the IM3 product at (f.sub.2 -f.sub.1)+f.sub.2 =882 MHz, and the IM2 product at (2.multidot.f.sub.2) mixes with the undesired signal at f.sub.1 to generate the IM3 product at (2.multidot.f.sub.2)-f.sub.1 =882 MHz. The third-order nonlinearity of the active circuit also generates an IM3 product at (2.multidot.f.sub.2 -f.sub.1)=882 MHz. As shown in FIG. 1A, three IM3 products (f.sub.2 -f.sub.1)+f.sub.2, (2.multidot.f.sub.2)-f.sub.1, and (2.multidot.f.sub.2 -f.sub.1) fall within the desired signal band.
The total amplitude of the combined IM3 product at the desired signal frequency f.sub.d depends on the magnitudes and phases of the individual IM3 products. In the worst case, all IM3 products have the same phase and add constructively, resulting in the maximum possible interfering signal (i.e., the largest IM3 distortion) at the desired frequency. The interfering signal behaves as noise that degrades the performance of the system in which the active circuit is used.
As can be seen, techniques that reduce the amplitude of the interfering IM3 products are highly desirable, especially in communications systems.